The sum of the series `Sigma_(r = 0)^(10) ""^(20)C_(r) " is " 2^(19) + (""^(20)C_(10))/(2)`

Explanation

To solve the problem, we need to find the sum of the series \( \sum_{r=0}^{10} \binom{20}{r} \) and show that it equals \( 2^{19} + \frac{\binom{20}{10}}{2} \).

### Step-by-Step Solution:

1. **Understanding the Binomial Theorem**:
The Binomial Theorem states that:
\[
(1 + x)^n = \sum_{r=0}^{n} \binom{n}{r} x^r
...